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Faculty of Information Engineering & TechnologyElectrical & Electronics DepartmentCourse: Digital Logic Design [ELCT 201]Assignment 1Dr. Ahmed MadianDr. Rania SweifName: ______________________ Group:______ ID:________1. For the following Boolean expressions simplify using Booleanalgebra and implement with basic logic gates? Which twoexpressions have the same simplified function?1

2. Simplify the following function and implement withbasic logic gates:F(A,B,C,D ) = (4,5,6,13,15)2

3. Design a circuit with output f and input A, B, C , and D. Let the twoinputs AB represent a two-bit number with A as the high order bit, andCD represent another two-bit number. That is, the values of AB representfour values 00(0), 01(1), 10 (2), 11 (3). The output f should be 1 only ifthe number represented by AB is greater than or equal to the numberrepresented by CD.a. Draw the truth tableb. Show the function F in form of POS.c. Implement the simplified form using basic logic gates3

4. F(A,B,C,D) = (0,2,4,5,6,9,10)+ d(7,11,12,13,14,15)Using K-Maps, simplify the above function and implement itusing logic gates:i) to the minimal Product-of-Sums (POS).F(A,B,C,D) =ii) To the minimal Sum-of-Products (SOP).F(A,B,C,D) =4

5. Show the Karnaugh map for F (A,B,C,D)=Σ(0,1,2,4,5,6,8,9,13,15). Listall prime implicants. Which prime implicants are essential?Prime implicants (all): ______________________________Essential prime implicants: _____________________________6. Show the Karnaugh map for and obtain a minimized Booleanexpression for F.F (A,B,C,D)=A’B’CD + ABCD’ + AB’C’D’ + ABC’D’+ ABC’D + ABCDF (A,B,C,D) =5

7. For the logic circuit shown below, find the logic function F, minimizeit and implement the minimized version using basic logic gates.6

8. System - Still Under Construction.Here's a solar heating system representation.The sun shines out of an intense blue sky onto a solar collector.The solar collector heats up.Fans can be used to move the accumulated heat in the collector to a rockbin - to store heat - or to the house itself.o Fan A can be used to move air through the solar collector.o Fan B can be used to move air into the heated space (the house).The way the system works is:When either fan is OFF, air cannot move through that fan.When both Fan A and Fan B are ON air moves through the collectordirectly into the house.When Fan B is ON and Fan A is OFF air moves from the rock bin intothe heated space.When Fan A is ON and Fan B is OFF (heated) air moves from thecollector to the rock bin.Several sensors are available, producing several signals.When the heated area needs heat the signal H becomes TRUE. Thissignal is supplied by a temperature sensor that compares measuredtemperature to desired temperature.When the rock bin is warmer than the heated space - and can supplyheat - a signal RH is TRUE. The measurements from two temperaturesensors is compared to generate this signal, and the same scheme isused for the two measurements below.When the collector is warmer than the heated space thesignal CH is TRUE.When the collector is warmer than the rock bin the signal CR is TRUE.7

a) Generate a truth table for all functions. Here is a blank truth table. FA is TRUEwhen Fan A is ON, and FB is TRUE when Fan B is ON. First, we note that whenthere is no need for heat to the heated space (H = 0), and the collector is warmerthan the rock bin (CR = 1) we should move heat from the collector to the rock bin.To do that, turn FAN A ON and B OFF.H RH CH CR FA FB0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 18

) However, there is one situation here that is thought-provoking. If CR = 1(Collector warmer than the Rock bin), and if RH = 1 (Rock bin warmer than theHeated space.), then it is clear that CH = 1 (Collecter warmer than the Heatedspace.) There are places in the truth table where that is not the case, and when CH= 0 in that situation, it's something that can't happen. Since it can't happen, wedon't care what the function is for that case. That gives us a new truth table withDON'T CAREs. We'll add DON'T CAREs wherever that happens. Complete truthtableH RH CH CR FA FB0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 1c) Implement the circuit for parts (a) and (b) using Basic logic gates.9